Question

A current of $2\text{A}$ flows through a $2\Omega$ resistor when connected across a battery. The same battery supplies a current of $0.5\text{A}$, when connected across a $9\Omega$ resistor. The internal resistance of the battery is:

​​​​​​​$[$1 Mark$]$

• A. $0.5\Omega$
• B. $\frac{1}{3}\Omega$
• C. $\frac{1}{4}\Omega$
• D. $1\Omega$

Answer 1

The correct option is B $\frac{1}{3}\Omega$

Let the internal resistance of battery be $r$
Case 1:- When battery connected across $2\Omega$ resistor

Using ohm's law

$E=2(2+r)\dots \left(1\right)$

Case 2 :- When battery connected across $9\Omega$ resistor


Using ohm's law

$E=0.5(9+r)\dots \left(2\right)$

from equation (1) and (2)

$2(2+r)=0.5(9+r)$

$4+2r=4.5+0.5r$

$1.5r=0.5$

$r=\frac{1}{3}\Omega$

$\therefore$ option $\left(b\right)$ is correct